\u4ee5\u4e0b\u306e\u554f\u306b\u7b54\u3048\u3088.<\/p>\r\n
(1)<\/strong>\u3000\u8907\u7d20\u6570 \\(\\alpha , \\beta\\) \u306b\u5bfe\u3057\u3066 \\(\\alpha \\beta = 0\\) \u306a\u3089\u3070, \\(\\alpha =0\\) \u307e\u305f\u306f \\(\\beta =0\\) \u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n (2)<\/strong>\u3000\u8907\u7d20\u6570 \\(\\alpha\\) \u306b\u5bfe\u3057\u3066 \\(\\alpha^2\\) \u304c\u6b63\u306e\u5b9f\u6570\u306a\u3089\u3070, \\(\\alpha\\) \u306f\u5b9f\u6570\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n (3)<\/strong>\u3000\u8907\u7d20\u6570 \\(\\alpha _ 1 , \\alpha _ 2 , \\cdots , \\alpha _ {2n+1}\\) \uff08 \\(n\\) \u306f\u81ea\u7136\u6570\uff09\u306b\u5bfe\u3057\u3066, \\(\\alpha _ 1 \\alpha _ 2 , \\alpha _ 2 \\alpha _ 3 , \\cdots , \\alpha _ {2n} \\alpha _ {2n+1}\\) \u304a\u3088\u3073 \\(\\alpha _ {2n+1} \\alpha _ 1\\) \u304c\u3059\u3079\u3066\u6b63\u306e\u5b9f\u6570\u3067\u3042\u308b\u3068\u3059\u308b. \u3053\u306e\u3068\u304d, \\(\\alpha _ 1 , \\alpha _ 2 , \\cdots , \\alpha _ {2n+1}\\) \u306f\u3059\u3079\u3066\u5b9f\u6570\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n<\/ol>\r\n (1)<\/strong><\/p>\r\n \\(\\alpha =a+bi , \\, \\beta =c+di\\) \uff08 \\(a , b , c , d\\) \u306f\u5b9f\u6570\uff09\u3068\u304a\u304f\u3068\r\n\\[\r\n\\alpha \\beta = (ac-bd) +(ad+bc)i = 0\r\n\\]\r\n\u3059\u306a\u308f\u3061\r\n\\[\r\nac-bd = 0 , \\, ad+bc = 0\r\n\\]\r\n\u3053\u308c\u3092\u7528\u3044\u308c\u3070\r\n\\[\\begin{gather}\r\n(ac-bd)^2 +(ad+bc)^2 = 0 \\\\\r\na^2c^2 +b^2d^2 +a^2d^2 +b^2c^2 = 0 \\\\\r\n\\text{\u2234} \\quad (a^2+b^2)(c^2+d^2) = 0\r\n\\end{gather}\\]\r\n\u3086\u3048\u306b\r\n\\[\r\na=b=0 \\ \\text{\u307e\u305f\u306f} \\ c=d=0\r\n\\]\r\n\u3088\u3063\u3066\r\n\\[\r\n\\alpha = 0 \\ \\text{\u307e\u305f\u306f} \\ \\beta = 0\r\n\\]\r\n (2)<\/strong><\/p>\r\n \\(\\alpha = a+bi\\) \uff08 \\(a , b\\) \u306f\u5b9f\u6570\uff09\u3068\u304a\u304f\u3068\r\n\\[\r\n\\alpha^2 = a^2 -b^2 +2abi\r\n\\]\r\n\u3053\u308c\u304c\u6b63\u306e\u5b9f\u6570\u306a\u306e\u3067\r\n\\[\r\na^2 -b^2 \\gt 0 , \\ ab = 0\r\n\\]\r\n\\(a = 0\\) \u3068\u4eee\u5b9a\u3059\u308b\u3068, \\(-b^2 \\gt 0\\) \u306f\u89e3\u3092\u3082\u305f\u305a, \u4e0d\u9069\u306a\u306e\u3067\r\n\\[\r\na \\neq 0 \\ \\text{\u304b\u3064} \\ b=0\r\n\\]\r\n\u3088\u3063\u3066, \\(\\alpha\\) \u306f \\(0\\) \u3067\u306a\u3044\u5b9f\u6570\u3067\u3042\u308b.<\/p>\r\n (3)<\/strong><\/p>\r\n \\(A =\\alpha _ 1 \\alpha _ 2 \\cdot \\alpha _ 2 \\alpha _ 3 \\cdot \\cdots \\alpha _ {2n} \\alpha _ {2n+1} \\cdot \\alpha _ {2n+1} \\alpha _ 1\\) \u3068\u304a\u304f\u3068\r\n\\[\\begin{align}\r\nA & = \\alpha _ 1^2 \\alpha _ 2^2 \\cdots {\\alpha _ {2n}}^2 {\\alpha _ {2n+1}}^2 \\\\\r\n& = {\\alpha _ 1}^2 ( \\alpha _ 2 \\alpha _ 3 )^2 \\cdots ( \\alpha _ {2n} \\alpha _ {2n+1})^2\r\n\\end{align}\\]\r\n\u3053\u3053\u3067, \\(( \\alpha _ 2 \\alpha _ 3 )^2 , \\cdots , ( \\alpha _ {2n} \\alpha _ {2n+1} )^2\\) \u3068 \\(A\\) \u306f\u3059\u3079\u3066\u6b63\u306e\u5b9f\u6570\u306a\u306e\u3067, \\({\\alpha _ 1}^2\\) \u3082\u6b63\u306e\u5b9f\u6570\u3067\u3042\u308b.
\r\n\r\n\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n
\r\n\u3086\u3048\u306b, (2)<\/strong> \u306e\u7d50\u679c\u3088\u308a, \\(\\alpha _ 1\\) \u306f\u5b9f\u6570.\r\n\u540c\u69d8\u306b\u3059\u308c\u3070, \\(\\alpha _ 2 , \\cdots , \\alpha _ {2n+1}\\) \u3082, \u5b9f\u6570\u3067\u3042\u308b\u3053\u3068\u304c\u793a\u305b\u308b\u306e\u3067, \u984c\u610f\u306f\u793a\u3055\u308c\u305f.<\/p>\r\n","protected":false},"excerpt":{"rendered":"\u4ee5\u4e0b\u306e\u554f\u306b\u7b54\u3048\u3088. (1)\u3000\u8907\u7d20\u6570 \\(\\alpha , \\beta\\) \u306b\u5bfe\u3057\u3066 \\(\\alpha \\beta = 0\\) \u306a\u3089\u3070, \\(\\alpha =0\\) \u307e\u305f\u306f \\(\\beta =0\\) \u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b. ( … \u7d9a\u304d\u3092\u8aad\u3080